Synchronisation in networks of delay-coupled type-I excitable systems

We use a generic model for type-I excitability (known as the SNIPER or SNIC model) to describe the local dynamics of nodes within a network in the presence of non-zero coupling delays. Utilising the method of the Master Stability Function, we investigate the stability of the zero-lag synchronised dynamics of the network nodes and its dependence on the two coupling parameters, namely the coupling strength and delay time. Unlike in the FitzHugh-Nagumo model (a model for type-II excitability), there are parameter ranges where the stability of synchronisation depends on the coupling strength and delay time. One important implication of these results is that there exist complex networks for which the adding of inhibitory links in a small-world fashion may not only lead to a loss of stable synchronisation, but may also restabilise synchronisation or introduce multiple transitions between synchronisation and desynchronisation. To underline the scope of our results, we show using the Stuart-Landau model that such multiple transitions do not only occur in excitable systems, but also in oscillatory ones.Comment: 10 pages, 9 figure

Statistical Analysis of Membrane Potential Fluctuations Relation with Presynaptic Spike Train

In a study of integration at the single neuron level, the relationships between the postsynaptic membrane potential and the presynaptic spike train were analyzed. Fluctuations in membrane potential of neurons in the visceral ganglion of Aplysia were measured and described by histograms. The histogram estimates the probability density function of the membrane potential. Comparisons were made among histograms when there was no synaptic input, and when there was a single input in which variations were made in the PSP (postsynaptic potential) sign, i.e. excitatory or inhibitory, and arrival statistics, e.g. slow or fast, regular, Poisson-like, or patterned. This was examined in cells where the membrane potential was constant and in cells in which there was spontaneous pacemaker activity. The form of the histogram depended on whether the neuron was spontaneously quiescent or a pacemaker, or whether it received presynaptic input and, if it did, on the sign and temporal characteristics of such input. From such histograms the mean firing rate of output spike trains can be predicted; additional information of a temporal nature is required, however, to predict features of the interval structure of the output train. Suggestions are made concerning the way the nervous system might utilize the information summarized in the membrane potential histogram